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Marge Lial has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.
David Schneider has taught mathematics at universities for over 34 years and has authored 36 books. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. During most of his professional career, he was on the faculty of the University of Maryland--College Park. His hobbies include travel, dancing, bicycling, and hiking.
Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks on an athletic scholarship, playing both basketball and tennis. While there, she earned a bachelor’s degree in Secondary Mathematics Education as well as the NAIA Academic All-American Award. She has two master’s degrees: one in Applied Mathematics and Statistics from the University of Missouri-Rolla, the second in Adult Education from the University of Missouri- St. Louis. Her hobbies include watching her sons play sports, riding horses, fishing, shooting photographs, and playing guitar. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students’ understanding of mathematics, and creating materials that support classroom teaching and student understanding.
Table of Contents
1. Trigonometric Functions
1.2 Angle Relationships and Similar Triangles
1.3 Trigonometric Functions
1.4 Using the Definitions of the Trigonometric Functions
2. Acute Angles and Right Triangles
2.1 Trigonometric Functions of Acute Angles
2.2 Trigonometric Functions of Non-Acute Angles
2.3 Finding Trigonometric Function Values Using a Calculator
2.4 Solving Right Triangles
2.5 Further Applications of Right Triangles
3. Radian Measure and the Unit Circle
3.1 Radian Measure
3.2 Applications of Radian Measure
3.3 The Unit Circle and Circular Functions
3.4 Linear and Angular Speed
4. Graphs of the Circular Functions
4.1 Graphs of the Sine and Cosine Functions
4.2 Translations of the Graphs of the Sine and Cosine Functions
4.3 Graphs of the Tangent and Cotangent Functions
4.4 Graphs of the Secant and Cosecant Functions
4.5 Harmonic Motion
5. Trigonometric Identities
5.1 Fundamental Identities
5.2 Verifying Trigonometric Identities
5.3 Sum and Difference Identities for Cosine
5.4 Sum and Difference Identities for Sine and Tangent
5.5 Double-Angle Identities
5.6 Half-Angle Identities
6. Inverse Circular Functions and Trigonometric Equations
6.1 Inverse Circular Functions
6.2 Trigonometric Equations I
6.3 Trigonometric Equations II
6.4 Equations Involving Inverse Trigonometric Functions
7. Applications of Trigonometry and Vectors
7.1 Oblique Triangles and the Law of Sines
7.2 The Ambiguous Case of the Law of Sines
7.3 The Law of Cosines
7.4 Vectors, Operation, and the Dot Product
7.5 Applications of Vectors
8. Complex Numbers, Polar Equations, and Parametric Equations
8.1 Complex Numbers
8.2 Trigonometric (Polar) Form of Complex Numbers
8.3 The Product and Quotient Theorems
8.4 De Moivre's Theorem; Powers and Roots of Complex Numbers
8.5 Polar Equations and Graphs
8.6 Parametic Equations, Graphs, and Applications
Appendix A. Equations and Inequalities
Appendix B. Graphs of Equations
Appendix C. Functions
Appendix D. Graphing Techniques
Solutions to Selected Exercises
Answers to Selected Exercises
Index of Applications